Magnetic resonance imaging (MRI) is a non-invasive diagnostic imaging procedure that uses nuclear magnetization and radio waves to produce internal images of a patient. Briefly, an MRI scanner contains magnetic coils that create a strong static magnetic field in which the patient is positioned. Certain atoms in a patient's body that were previously randomly-ordered become aligned along the magnetic field. The scanner then sends a series of bursts or pulses of radio frequency (RF) energy through the patient's body part under examination that excite the “ordered” atoms to a specific oscillation around the magnetic field. The atoms give up the RF energy, i.e., generate an RF signal, each time the atoms return to their respective alignments during the oscillation. The scanner detects the RF signals by appropriate reception or pick-up coils and uses gradient coils to generate non-homogeneous magnetic fields to enable the signals to be spatially coded in all three spatial directions. The scanner processes the coded signals or data to transform them into a visual representation of the patient's body part. In particular, the scanner digitizes the signals, creates a so-called k-space matrix (frequency domain data) filled with the digitized complex values of each signal, and generates for display and/or other usage a corresponding MR image from the k-space matrix by means of a complex Fourier transformation. The MRI scanner acquires three-dimensional image data of the patient's body part for respective “slices” of an area of the body part. The scanner repeats a pre-defined MR image pulse sequence, i.e., the above-described steps for collecting the signals/data, a number of times to collect sufficient data from the excitations to reconstruct the specific image. Ideally, there are little or no variations in the nuclear magnetization during the excitations. However, movement by the patient, voluntary or involuntary, may affect the nuclear magnetization and the subsequent MR image reconstruction.
In fact, motion artifacts due to patient motion during the image acquisition are a very common problem in MRI. Motion artifacts, especially those caused by large motions, can significantly degrade the quality of MR images (e.g., ghosting and/or blurring. As described above, in MRI, time signals of an imaged patient or subject are produced by controlling a sequence of RF pulses and time-varying gradient magnetic fields. Matching a time signal to the location of its source generates image data known as spatial encoding. This can be accomplished because variations in the magnetic field cause the time signals to have frequencies that are functions of position. These time signals are acquired during scanning and thereafter mapped into a 2-D array, i.e. the k-space. The time signals are acquired by a line readout along the x-direction in separate scans and the line readout signals are collected row by row to fill the k-space. Normally, the x-direction is referred to as the frequency encoding (FE) direction while the y-direction is referred to as the phase encoding (PE) direction. A reconstruction algorithm, most often the inverse Fourier transform (IFT), is then used to convert the k-space information to an image of the patient or subject. Data acquisition is extremely rapid in the FE direction (msec/degree) so motion can be largely ignored. The time intervals in the PE direction are much longer (sec/degree). Therefore, inconsistencies that exist in k-space due to patient motion (in the form of phase shifts) occur between lines in the PE direction. Motion artifacts in the subject image are a consequence of these phase shifts. Removing motion artifacts is usually then formulated as recovering phase information in the frequency domain.
Many methods and devices have been developed to remove patient or subject motions and restore MR images. Some directly measure motion. For example, navigation-echo is a traditional technique for handling patient or subject motions. Briefly, an echo signal (“navigator” echo) is introduced to pass through the center of the data space i.e., k-space, and phase variations are detected by use of further signal processing and reconstruction algorithms. Computational methods are then used to correct the undesired view-to-view phase variations and eliminate a significant source of motion artifacts in an image. The navigator echo method is more fully described in an article by R. L. Ehman and J. P. Felmlee, “Adaptive technique for high-definition MR imaging of moving structures”, Radiology vol. 173, no. 1, pp. 255-263, October 1989. However, the navigation-echo technique requires some special pulse sequences which are not available in all commercial scanners or for all applications. In another technique, motion is estimated by attaching external markers to the imaged subject; but this approach may not be practical in all applications. This is more fully described in an article by A. S. Fahmy, B. Tawtik, and Y. M. Kadah, “Robust estimation of planar rigid body motion in magnetic resonance imaging”, Proc. International Conference on Image Processing, vol. 2, 2000, pp. 487-490 vol. 2.
Another method to address motion artifacts uses techniques to observe the features of images to determine patient motions. This type of method does not require special scanners or special pulse sequences. Instead, this method needs a good metric which can measure the quality of images. Examples are entropy criterion (described in the article by D. Atkinson, D. L. G. Hill, P. N. R. Stoyle, P. E. Summers, and S. F. Keevil, “Automatic correction of motion artifacts in magnetic resonance images using an entropy focus criterion”, IEEE Transactions on Medical Imaging, vol. 16, no. 6, pp. 903-910, 1997 and the article by D. Atkinson, D. L. Hill, P. N. Stoyle, P. E. Summers, S. Clare, R. Bowtell, and S. F. Keevil, “Automatic compensation of motion artifacts in MRI”, Magnetic Resonance in Medicine, vol. 41, no. 1, pp. 163-170, January 1999) and normalized gradient squared (NGS) (described in the article by A. Manduca, K. P. McGee, E. B. Welch, J. P. Felmlee, R. C. Grimm, and R. L. Ehman, “Autocorrection in MR imaging: adaptive motion correction without navigator echoes”, Radiology, vol. 215, no. 3, pp. 904-909, June 2000). Some image metric-based techniques have been employed in clinical settings and their results are comparable with the navigator-echo techniques. An evaluation of various metrics is described in an article by K. P. Mcgee, A. Manduca, J. P. Felmlee, S. J. Riederer, and R. L. Ehman, “Image metric-based correction (autocorrection) of motion effects: Analysis of image metrics”, Journal of Magnetic Resonance Imaging, vol. 11, no. 2, pp. 174-181, 2000. These metrics are mainly global image metrics which are applied to the whole image to compute a single score.
An important issue in the image metric-based method is the optimization procedure, i.e., how to minimize the image metric. In one technique, the rows of MR signals data (k-space) are grouped into several intervals. For each interval, the motions (dx, dy) in {−m·s,−(m−1)·s, . . . , m·s}×{−m·s,−(m−1)·s, . . . , m·s} are evaluated with an image metric. Then, the motion with the best image quality measure is selected as the motion associated with the segment and is also applied to compensate the motion artifact at this segment. The efficiency of the algorithm depends on the size of the so-called metric map. This is described more fully in the first article noted above by D. Atkinson, et al. In another technique, a systematic approach, called center-out, is used to find the motion and compensate for the motion artifact sequentially from the center to outer segments. This is described more fully in the second article noted above by D. Atkinson, et al. Another optimization technique replaces the normalized gradient squared (NGS) measure by the entropy measure to find a pattern in the NGS metric map that can be used to reduce the evaluations in NGS. However, this technique is too rough and simply using the mentioned metrics may easily fail to correct the MR images with motion artifacts due to large motions. More recently, a more sophisticated image metric-based method, called EXTRACT, has been described that is based on extrapolation of the k-space data and the metric is the correlation value between extrapolated k-space data and a tested k-space data. This is described more fully in an article by W. Lin, and H. K. Song, “Extrapolation and correlation (EXTRACT): a new method for motion compensation in MRI”, IEEE Transactions on Medical Imaging, vol. 28, Issue 1, January 2009, pp 82-93.
The image metric-based methods generate a set of trial motions for each PE scan and the best motion is selected after evaluating the values of image metrics for all trial motions. Several techniques have been applied to minimize the image metrics and they perform well for small motions. Generally, however, due to high dimensionality of the search space and the complicated image metrics, the correct minimizer is hard to locate when the original MR signals are corrupted by large motions.
The MRI motion artifact compensation problem is similar to the blind image restoration problem where the goal is to estimate the corruption-free image and the blur (i.e., motion point spread function (PSF)) kernel from the MR image with motion artifacts with the motion PSF being unknown. According to convolution theorem, the IFT of the observed k-space data is the convolution of the IFT of the corruption-free k-space data and a kernel which is the IFT of the phase shift as mentioned above. Although this problem formulation is similar to blind image restoration, state-of-the-art de-blurring or deconvolution methods can not be applied because this kernel is a complex matrix and its size is as large as the size of the k-space data, i.e., the image size. In addition, the kernel for MRI motion artifacts has a specific form.